The City of New York (comprising all five counties or "boroughs") is referred to as New York, NY. The island and borough of Manhattan is New York, NY. When you write a letter to someone in Manhattan,...
Just to add: If you go to Penn Station, you can take Amtrak to Rhinecliff, NY, which is a hamlet outside of Rhinebeck and then take a cab into town.
If you go to Grand Central, you would take...